Power System Dynamic Model Research Articles

Leveraging Pumped Storage Power Plants for Innovative Stability Enhancement of Weakly Interconnected Power Systems

The hybrid AC/DC grid, based on a significant share of renewable energy sources, is gradually becoming an essential aspect of the modern energy system. The integration of intermittent renewable generators into contemporary energy systems is accompanied by the decommissioning of power plants containing synchronous generators. Consequently, this leads to a reduction in system inertia and an increase in the risk of stability disruption. The abrupt disconnection of the primary generator or power line can result in an unanticipated mismatch between power generation and consumption. This discrepancy can trigger substantial and swiftly evolving alterations in power distribution, angular speed, load flow, and the frequency of generators. The risks of an energy system collapse can be mitigated through automation, enabling rapid adjustments to generation and load capacities, as well as power flows, in the electrical network. This article justifies the utilisation of a power control method for high-voltage power line interconnections. The technology of hydro storage power plants and measurements of voltage phasors are employed. The potential for easing power flow restrictions and realising substantial economic benefits is supported by the results obtained using simplified dynamic model of the Baltic power system and Nord Pool electricity market model.

Hybrid Power System Design and Dynamic Modeling for Enhanced Reliability in Remote Natural Gas Pipeline Control Stations

The most rapid and efficient method to transport natural gas from its source to its destination is through a pipeline network. The optimal functioning of control stations for natural gas pipelines depends on the use of electrical devices, including data loggers, communication devices, control systems, surveillance equipment, and more. Ensuring a reliable and consistent power supply proves to be challenging due to the remote locations of these control stations. This research article presents a case study detailing the design and dynamic modeling of a hybrid power system (HPS) to address the specific energy needs of a particular natural gas pipeline control station. The HOMER Pro 3.17.1 software is used to design an optimal HPS for the specified location. The designed system combines a photovoltaic (PV) system with natural gas generators as a backup to ensure a reliable and consistent power supply for the control station. Furthermore, it provides significant cost savings, reducing the cost of energy (COE) by USD 0.148 and the annual operating costs by USD 87,321, all while integrating a renewable energy fraction of 79.2%. Dynamic modeling of the designed system is performed in MATLAB/Simulink R2022a to analyze the system’s response, including its power quality, harmonics, voltage transients, load impact, etc. The experimental results are validated using hardware in the loop (HIL) and OPAL-RT Technologies’ real-time OP5707XG simulator.

Grid Forming Technologies to Improve Rate of Change in Frequency and Frequency Nadir: Analysis-Based Replicated Load Shedding Events

Electric power generation is quickly transitioning toward nontraditional inverter-based resources (IBRs). Prevalent devices today are solar PV, wind generators, and battery energy storage systems (BESS) based on electrochemical packs. These IBRs are interconnected throughout the power system via power electronics inverter bridges, which have sophisticated controls. This paper studies the impacts and benefits resulting from the integration of grid forming (GFM) inverters and energy storage on the stability of power systems via replicating real events of loss of generation units that resulted in large load shedding events. First, the authors tuned the power system dynamic model in Power System Simulator for Engineering (PSSE) to replicate the event records and, upon integrating the IBRs, analyzed the system dynamic responses of the BESS. This was conducted for both GFM and grid following (GFL) modes. Additionally, models for Grid Forming Static Synchronous Compensator (GFM STATCOM), were also created and simulated to allow for quantifying the benefits of this technology and a techno-economic analysis compared with GFM BESSs. The results presented in this paper demonstrate the need for industry standardization in the application of GFM inverters to unleash their benefits to the bulk electric grid. The results also demonstrate that the GFM STATCOM is a very capable system that can augment the bulk system inertia, effectively reducing the occurrence of load shedding events.

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. The comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

Bulk Power Systems Emergency Control Based on Machine Learning Algorithms and Phasor Measurement Units Data: A State-of-the-Art Review

Modern electrical power systems are characterized by a high rate of transient processes, the use of digital monitoring and control systems, and the accumulation of a large amount of technological information. The active integration of renewable energy sources contributes to reducing the inertia of power systems and changing the nature of transient processes. As a result, the effectiveness of emergency control systems decreases. Traditional emergency control systems operate based on the numerical analysis of power system dynamic models. This allows for finding the optimal set of preventive commands (solutions) in the form of disconnections of generating units, consumers, transmission lines, and other primary grid equipment. Thus, the steady-state or transient stability of a power system is provided. After the active integration of renewable sources into power systems, traditional emergency control algorithms became ineffective due to the time delay in finding the optimal set of control actions. Currently, machine learning algorithms are being developed that provide high performance and adaptability. This paper contains a meta-analysis of modern emergency control algorithms for power systems based on machine learning and synchronized phasor measurement data. It describes algorithms for determining disturbances in the power system, selecting control actions to maintain transient and steady-state stability, stability in voltage level, and limiting frequency. This study examines 53 studies piled on the development of a methodology for analyzing the stability of power systems based on ML algorithms. The analysis of the research is carried out in terms of accuracy, computational latency, and data used in training and testing. The most frequently used textual mathematical models of power systems are determined, and the most suitable ML algorithms for use in the operational control circuit of power systems in real time are determined. This paper also provides an analysis of the advantages and disadvantages of existing algorithms, as well as identifies areas for further research.

Advantage of battery energy storage systems for assisting hydropower units to suppress the frequency fluctuations caused by wind power variations

The integration of renewable energy sources into power grids has led to new challenges for maintaining the frequency stability of power systems. Hydropower has traditionally played a key role in frequency regulation due to its flexibility in output power. However, the water hammer effect can lead to the phenomenon of inverse regulation, which can degrade the transient characteristics of power systems, particularly in hydropower-dominant systems, such as the Southwest China Power Grid. On the other hand, battery energy storage systems (BESSs) are well-suited for frequency regulation due to their fast response speed, high response accuracy, and flexible control capabilities. Hence, it is a meaningful topic to evaluate the advantage of integrated battery energy storage systems for assisting hydropower units (HPUs) in frequency regulation. First, the frequency dynamic response model of power system with BESSs assisting HPUs to participate in frequency regulation is established. Then, a two-part strategy is presented. The primary frequency regulation strategy for BESSs uses droop control with a variable regulation coefficient and the secondary frequency regulation strategy considers the costs associated with both HPUs and BESSs. Last, a performance assessment is carried out based on the management rules for auxiliary services of power plants in China and the USA. The results of this study demonstrate that the incorporation of the BESS into the HPU can significantly improve the regulating performance, and can provide important economic and technical benefits for the power system. Specifically, the maximum ratio of HPU with BESS to conventional HPU is 33.13 %, 33.85 %, 7.60 % and 41.52 % for the different indicators (difference, delay, distance, and cost). Notably, the implementation of BESS in the HPU not only contributes to the stability of the power system, but it also provides considerable economic benefits by achieving higher evaluations for auxiliary services in the power market. These findings are critical in supporting the transformation and development of conventional HPUs under large-scale new energy grid connection conditions.

Data-driven modeling of power system dynamics: Challenges, state of the art, and future work

Data-driven modeling of power system dynamics: Challenges, state of the art, and future work

A Novel Small Disturbance Stochastic Stability Analysis Method Based on Entropy

Power system stability has become an increasing concern in renewable power integration because the active power generated by renewable energy varies randomly. Thus, we focus on random outside excitations in this study. Since the power obeys Non‐Gaussian distribution in most case, a novel small disturbance stochastic stability analysis method based on entropy is presented. First, the dynamic model of power system with random outside excitation is established by stochastic differential equation. Then, the values of mean and mean square stability are efficiently derived by transforming the stochastic differential equation into a deterministic mean or variance equation. For non‐Gaussian disturbance, entropy stability is presented by this transformation. At last, the numerical simulations are presented on a WSCC three‐generator nine‐bus power system with a wind farm © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Hierarchical optimal allocation of BESS using APT-FPSO based on stochastic programming model considering voltage sensitivity and eigenvalues analyses

Integration of energy storage systems (ESSs) to microgrids (MGs) due to the growing penetration of intermittent energy resources is a great motivation to develop studies in the context of optimal sizing and placement of these systems. In this paper, a multi-objective bi-level optimization problem is addressed based on the stochastic nature and dynamic model of power system elements.As a preliminary step, the optimal size and capacity of the battery energy storage system (BESS) are determined to minimize frequency fluctuations. This level has been performed based on three approaches considering the daily intra-hour stochastic data. In the secondary level, the dynamic behaviour of all MG elements has been considered and correspondingly a dynamic objective function based on system eigenvalues and voltage sensitivity index (VSI) has been developed. According to the proposed objective function, the secondary step for sizing and placement of the battery units has been performed by adaptive particularly tuneable fuzzy particle swarm optimization (APT-FPSO) algorithm to reduce power losses, improve the voltage profile/ stability, and mitigate low-frequency fluctuations. Finally, the effectiveness of the proposed approach is evaluated using time-domain simulations, voltage sensitivity studies, and eigenvalue analysis.

A human operator model for simulation-based resilience assessment of power grid restoration operations

Human operations play a vital role for the resilience of power grids. While past research concentrated on performance in cascading failures, this work proposes a system model that focuses on assessing the impact of the performance of operators in grid operations and restorations. The operator model developed for this purpose addresses human performance and variability by accounting for stochastic durations, potential errors and alternative responses, and the probabilities of these outcomes. Discrete event simulation is the assessment framework, with the model implemented in MATLAB Simulink in conjunction with a dynamic power system model. A re-energization cell provided by a Swiss generation system operator is used for a case study demonstration of the simulation model, which produces distributions of the total restoration duration and restoration success rates while identifying the parts of restoration plans that could be modified to enhance restoration performance. The overall outcomes of the case study suggest that the human element can be treated practically in grid simulations in order to produce findings that will increase grid resilience.

Resilient distributed model‐free adaptive predictive control for multiarea power systems under denial of service attack

AbstractThis paper proposes a novel load frequency control (LFC) strategy for power systems based on distributed model‐free adaptive predictive control. First, a power system dynamic model is established by the input and output signals of the power system. Then, a distributed model‐free adaptive predictive control algorithm is established for the power system under denial‐of‐service attack by the established power system dynamic model, and a predictive compensation algorithm is designed to compensate the impact of DoS attack. Based on the designed distributed model‐free adaptive predictive control algorithm, the frequency tracking error of the multiarea power system is bounded. The scheme is independent of the structure of the power system and does not need to measure any state signals of the power system, relying only on the input and output data of the power system. The results of simulations demonstrate the effectiveness and superiority of the design.

Optimization of Power System Stabilizers Using Proportional-Integral-Derivative Controller-Based Antlion Algorithm: Experimental Validation via Electronics Environment

A robust, optimized power system stabilizer (PSS) is crucial for oscillation damping, and thus improving electrical network stability. Additionally, real-time testing methods are required to significantly reduce the likelihood of software failure in a real-world setting at the user location. This paper presents an Antlion-based proportional integral derivative (PID) PSS to improve power system stability during real-time constraints. The Antlion optimization (ALO) is developed with real-time testing methodology, using hardware-in-the-loop (HIL) that can communicate multiple digital control schemes with real-time signals. The dynamic power system model runs on the dSPACE DS1104, and the proposed PSS runs on the field programmable gate arrays (FPGA) (NI SbRIO-9636 board). The optimized PSS performance was compared with a modified particle swarm optimization (MPSO)-based PID-PSS, through different performance indices. The test cases include other step load perturbations and several short circuit faults at various locations. Twelve different test cases have been applied, through real-time constraints, to prove the robustness of the proposed PSS. These include 5 and 10% step changes through 3 different operating conditions and single, double, and triple lines to ground short circuits through 3 different operating conditions, and at various locations of the system transmission lines. The analysis demonstrates the effectiveness of ALO and MPSO in regaining the system’s stability under the three loading conditions. The integral square of the error (ISE), integral absolute of the error (IAE), integral time square of the error (ITSE), and integral time absolute of the error (ITAE) are used as performance indices in the analysis stage. The simulation results demonstrate the effectiveness of the proposed PSS, based on the ALO algorithm. It provides a robust performance, compared to the traditional PSS. Regarding the applied indices, the proposed PSS, based on the ALO algorithm, obtains significant improvement percentages in ISE, IAE, ITSE, and ITAE with 30.919%, 23.295%, 51.073%, and 53.624%, respectively.

Enhanced Primary Frequency Control Using Model Predictive Control in Large-Islanded Power Grids with High Penetration of DFIG-Based Wind Farm

A new primary frequency controller in power grids undergoing massive wind power penetration is the focus of this paper. The inescapable problem in a largely wind penetrated power grid is to ensure the maintenance of its frequency in the nominal band prescribed by the power system operator (PSO). However, with the massive arrival of wind farms with conventional control schemes, the operation of maintaining and restoring the frequency to the regulatory regimes remains very complicated. In order to overcome the above problem, this paper proposes a new strategy for primary frequency control in power grids using model predictive control (MPC) for a multi-cluster doubly-fed induction generator (DFIG)-based wind farm (WF), with a main objective of reducing the frequency nadir (FN), eliminating the second frequency dip (SFD), and providing the optimal support during wind speed variations. In this approach, a rolling prediction and optimization control strategy is developed based on the dynamic power system model to ideally predict the additional power to be provided. Moreover, in order to avoid second frequency dips, the wind turbines (WTs) are not allocated to extract additional power from the grid during the frequency event, the rotor speeds are not recovered to the maximum power point tracking (MPPT) operating points during the primary frequency control. The performance of the proposed controller was evaluated using a two-zone electrical system in MATLAB/Simulink®. The obtained results disclose that the frequency nadir is enhanced with more than 6.1% compared to the conventional schemes. In addition, the frequency response settling time has been improved with more than 10.51 s.

Feasibility Study of Neural ODE and DAE Modules for Power System Dynamic Component Modeling

In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential equations (ODE) module and a neural differential-algebraic equations (DAE) module are proposed to form a data-driven modeling framework that accurately captures components' dynamic characteristics and flexibly adapts to various interface settings. Secondly, analytical models and data-driven models learned by the neural ODE and DAE modules are integrated together and simulated simultaneously using unified transient stability simulation methods. Finally, the neural ODE and DAE modules are implemented with Python and made public on GitHub. Using the portal measurements, three simple but representative cases of excitation controller modeling, photovoltaic power plant modeling, and equivalent load modeling of a regional power network are carried out in the IEEE-39 system and 2383wp system. Neural dynamic model-integrated simulations are compared with the original model-based ones to verify the feasibility and potentiality of the proposed neural ODE and DAE modules.

On the Calculation of the Variance of Algebraic Variables in Power System Dynamic Models With Stochastic Processes

This letter presents a technique to calculate the variance of algebraic variables of power system models represented as a set of stochastic differential-algebraic equations. The technique utilizes the solution of a Lyapunov equation and requires the calculation of the state matrix of the system. The IEEE 14-bus system serves to demonstrate the accuracy of the proposed technique over a wide range of variances of stochastic processes. The accuracy is evaluated by comparing the results with those obtained with Monte Carlo time domain simulations. Finally, a case study based on a 1479-bus dynamic model of the all-island Irish transmission system shows the computational efficiency of the proposed approach compared to the Monte Carlo method.

Hierarchical Frequency Control of Hybrid Power Plants Using Frequency Response Observer

With frequency stability being challenged in modern power systems, transmission system operators have been designing new mitigation measures, such as fast frequency response (FFR), to maintain operation security of power systems. To accommodate technical requirements of new frequency control services (FCSs), the corresponding control should be implemented at asset controllers to enable fast responses. However, control counteraction can arise between plant controllers and asset controllers during the provision of FCSs. In this paper, a novel hierarchical frequency control approach is proposed to allow hybrid power plants (HPPs) to provide three types of FCSs, namely FFR, frequency containment response (FCR) and frequency restoration response (FRR). To solve control counteraction issue, an innovative frequency response observer (FROB) is proposed. The FROB at plant controllers and the hybrid power plant controller (HPPC) accurately estimates frequency response initiated by asset controllers, and the obtained estimation is used for control compensation at plant controllers and the HPPC to avoid control counteraction. Design guidelines and robustness analysis of the FROB are then discussed. Case studies are implemented in a power system dynamic model in MATLAB/Simulink, and the results show that the proposed frequency control approach enables coordinated operation of multiple technology power plants, with robust performance achieved when there are system uncertainties in HPPs.

Dynamic performance of the combined stirling thermoelectric conversion technology for a lunar surface nuclear power system

The space nuclear reactor power system is one of the most potential energy and power supplies for future lunar science exploration. Unlike the devices on Earth, the devices operating on the lunar surface require a higher level of intelligent and automatic system control. Thus, it is necessary to establish a comprehensive and accurate dynamic system model to improve the system's automatic control. In the present study, a dynamic system model of a lunar surface nuclear power system combined with a Stirling cycle was proposed. The dynamic system model consists of a reactor core model, a heat rejection model, and a Stirling thermoelectric conversion model (while the reactor core is simplified as a point heat source). MATLAB and Simulink platforms are applied to implement the system model. To verify the system model and analyze the dynamic performance, simulations of the several reactor startup processes, different reactor thermal power (reactivity disturbances), and different lunar surface temperature conditions were carried out. The results show that the effects of thermal power variation on the dynamic system model have a nonlinear delay. Furthermore, the lunar surface temperature significantly impacts the dynamic system's operation and response. The present study provides a practical tool for the transient analysis of the lunar surface nuclear reactor power system and theoretical support for the design of lunar surface nuclear reactors.

Feed-Forward Neural Network for health monitoring of a parallel hybrid electric power system

Hybrid engines are becoming more and more widespread. Electric energy instead is a valid help to reduce the environmental impact. In hybrid engines, the number of components is higher and this results in a decrease in reliability. With Engine Health Monitoring (EHM) we mean the set of techniques used to monitor the health status of a system based on the values assumed by some related parameters. Artificial Intelligence (AI) methods are widely used nowadays in this discipline. In this paper, an EHM approach was developed to monitor the health status of some components constituting an hybrid turboshaft. The dynamic model of the hybrid electric power system is described in an accompanying paper. Feed-Forward Neural Network (FFNN) is used as AI tool to built the just cited system. The engine modelled with Simulink, was used to perform a series of steady-state simulations implementing a degradation condition in some selected components. The degradation condition was simulated by changing the value of the Performance Parameters (PPs) related to each of the selected components. The results of the simulation were used to obtain a dataset useful to train the FFNN to predict the values of the same PPs in a degraded case.

Robustness Verification for Machine-Learning-Based Power System Dynamic Security Assessment Models Under Adversarial Examples

Based on machine learning (ML) technique, the data-driven power system dynamic security assessment (DSA) has received significant research interest. Yet, the well-trained ML-based models with high training and testing accuracy may be vulnerable to the adversarial example, which is a modified version of the original sample that is intentionally perturbed but retains being very close to the original one. Such adversarial examples can mislead the DSA results and lead to catastrophic consequences. Thus, the accuracy index alone is not enough to represent the performance of the ML-based DSA models. To evaluate the ML-based DSA models and provide formal robustness guarantee for real-time DSA, this article proposes an adversarial robustness verification method to quantify the ability of ML-based DSA models against all kinds of adversarial examples. A model-free and attack-independent robust index is defined for both differentiable and nondifferentiable attack scenarios. Simulation results have verified the effectiveness of the proposed adversarial robustness verification method and the superiority of robust index compared with the upper bound of the adversarial perturbations computed by existing adversarial attack methods.

Sliding Mode Control of Two-Parameter Fourth-Order Chaos Model of Power System

As a complex nonlinear system, the power system in operation may experience chaotic oscillation which can threaten the stability of the system for unexpected events and uncertain factors. Initially, through considering factors such as the generators, the power system node voltage amplitude and phase angle, this brief establishes a fourth-order power system dynamic model and a two-parameter fourth-order power system mathematical model with load reactive power and mechanical input power as chaotic parameters to explore the mechanism and characteristics of chaos in the power system with the chaos theory. In addition, a sliding mode controller based on exponential reaching law for four state variables is designed, which is used to suppress the chaotic oscillation of the power system and guarantee the system can work stably at the target operating point within the chaotic parameter range. The designed controller can effectively suppress the chaos in power system and has an ideal performance.